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A truck starts from rest and rolls down a hill with constant acceleration. It travels a distance of $400 m$ in $20 s$ . Find its acceleration and the force acting on it if its mass is $7$ tonnes.

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1 m / s^{2} and 2.8 \times 1 0^{4} N

2 m / s^{2} and 1.4 \times 1 0^{4} N

1 m / s^{2} and 1.4 \times 1 0^{4} N

2 m / s^{2} and 2.8 \times 1 0^{4} N

answer is B.

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Detailed Solution

Acceleration and Force acting on it, if its mass is

7

tonnes is

2 m / s^{2}

and

1.4 \times 1 0^{4} N

.
Given, that the truck starts from rest, its initial velocity,

u = 0

.
Distance,

s = 400 m

Time,

t = 20 s

Mass of the truck,

m = 7 tn

⇒

m = 7 \times 1 0^{3} kg

From Newton’s second law of motion,

s = ut + \frac{1}{2} a t^{2}

⇒

400 = 0 \times 20 + \frac{1}{2} \times a \times {(20)}^{2}

⇒

400 = 200 a

⇒

a = 2 m s^{- 2}

The force acting on the truck is,

F = ma

= 7 \times 10^{3} \times 2

= 14000 N

= 1.4 \times 10^{4} N

∴ The acceleration of the truck is

2 m / s^{2}

and the force acting on it is

1.4 \times 1 0^{4} N .

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